N. F. Morozov

Application of moment interaction to the construction of a stable model of graphite crystal lattice

The aim of the present paper is to construct and study a model of pair moment interaction between carbon atoms in the two-dimensional graphite lattice. The carbon atom is modeled by a structure consisting of three rigidly connected mass points located at the vertices of an equilateral triangle. The interaction between mass points is described by a pair force potential, but the total interatomic interaction contains moment components owing to the finite size of the structure modeling the atom. We compute rank 4 tensors characterizing the elastic properties of the graphite crystal lattice constructed on the basis of our model. We determine lattice stability criteria depending on the number of coordination spheres taken into account. We show that this model permits one to ensure stability of the graphite lattice but significantly underestimates the transverse-to-longitudinal interatomic coupling rigidity ratio. We construct a generalized moment potential that permits one to obtain a rigidity ratio consistent with experimental data.

Differential graphene resonator as a mass detector

We consider a fundamentally new scheme of graphene resonator, namely, a differential resonator, which provides a significantly increased sensitivity to the mass deposited on it. The differential resonator consists of two parallel graphene sheets located one over the other, the upper (basic) sheet and the lower (supplementary) sheet. The layers are fixed in supporting insulators, and the supplementary layer is located over the conducting surface. The power link between the layers is implemented by the electrostatic field in the space between the layers. Several equilibria are possible in such a mechanical system. The free vibration near the stable equilibrium are considered. The electric field strength in the space between the layers is chosen so that the mechanical system of two graphene layers has two close natural frequencies. The free vibrations of such a system exhibit beating. The characteristic frequency of the envelope, which is further called the beating frequency and is equal to half the difference of natural frequencies of the system, is much lower than the partial natural frequency of each layer. If a particle is deposited on the upper layer, then the partial natural frequency of this layer decreases. In this case, the characteristic frequency of the envelope changes, and a small variation in the partial natural frequency can lead to a significant change in the characteristic frequency of the envelope. This ensures that the differential resonator is more sensitive to the detected particle mass than single-layer resonators. The influence of various parameters of the differential resonator on the measurement accuracy is studied.

Beating in the problem of longitudinal impact on a thin rod

The longitudinal impact on an elastic rod generating a periodic system of longitudinal waves in the rod, is considered. For certain values of the problem parameters in the linear approximation, these waves generate parametric resonances accompanied by an infinite increase in the transverse vibrations amplitude. To obtain the finite values of the amplitudes, a quasilinear system where the influence of transverse vibrations on the longitudinal ones is taken into account was considered. Earlier, this system was solved numerically by the Bubnov—Galerkin method and the beatings accompanied by energy exchange between the longitudinal and transverse vibrations were obtained. Here an approximate analytic solution of this system based on two-scale expansions is constructed. A qualitative analysis is performed. The maximum transverse deflection depending on the loading method is estimated.

Oscillation stop as a way to determine spectral characteristics of a graphene resonator

A nanoresonator based on a graphene layer is investigated as an electromechanical oscillatory system. Mechanical oscillations are excited in it by a high-frequency alternating electric field. A nanoresonator is considered as a capacitor with kinematically varying capacity of the determined transverse deformation of the graphene layer as one of its plates. In the case of small ratios of energy accumulated in a capacitor to the amplitude of energy of mechanical oscillations and the time constant of the capacitor charge to the period of free oscillations, excitation of both common and parametric resonances is possible. It is shown that upon decreasing the external frequency lower than the half-frequency of free oscillations, the cessation of forced oscillations of the nanolayer is observed. This makes it possible to determine more reliably the variations in the intrinsic frequency of the nanoresonator upon deposition of a nanoparticle on it.

A differential graphene-based resonator

We describe a new, in principle, layout of a graphene resonator—a differential resonator, which makes it possible to increase substantially its sensitivity to the mass deposited on it. The differential resonator consists of two parallel graphene films, which are fastened in insulating supports; the lower film is arranged over the conducting surface. The force coupling between the films is performed by the electrostatic field in the space between them. Several equilibrium positions are possible in such a mechanical system. Small free oscillations near the stable equilibrium position are considered. The field strength is selected so that the mechanical system of two graphene films would have two close eigenfrequencies. The free oscillations of such a system have the form of intrinsic frequencies of the system much lower that the partial frequency of each film. When depositing the particle on the upper film, the partial eigenfrequency of this film decreases. In this case, the characteristic envelope frequency also decreases, and a small variation in the partial eigenfrequency leads to considerable variation in the characteristic envelope frequency. This provides higher sensitivity to the mass of the revealed particle for the differential resonator compared with the resonator based on one film.